Hypothesis Testing Approach to Detecting Collusion in Competitive Environments

There is growing concern about tacit collusion using algorithmic pricing, and regulators need tools to help detect the possibility of such collusion. This paper studies how to design a hypothesis testing framework in order to decide whether agents are behaving competitively or not. In our setting, agents are utility-maximizing and compete over prices of items. A regulator, with no knowledge of the agent's utility function, has access only to the agents' strategies (i.e., pricing decisions) and external shock values in order to decide if agents are behaving in competition according to some equilibrium problem. We leverage the formulation of such a problem as an inverse variational inequality and design a hypothesis test under a minimal set of assumptions. We demonstrate our method with computational experiments of the Bertrand competition game (with and without collusion) and show how our method performs.

[1]  Leen-Kiat Soh,et al.  Investigating reinforcement learning in multiagent coalition formation , 2004, AAAI 2004.

[2]  Ravindra K. Ahuja,et al.  Inverse Optimization , 2001, Oper. Res..

[3]  Frank Kelly,et al.  Charging and rate control for elastic traffic , 1997, Eur. Trans. Telecommun..

[4]  Ariel Ezrachi,et al.  Artificial Intelligence & Collusion: When Computers Inhibit Competition , 2015 .

[5]  Emilio Calvano,et al.  Artificial Intelligence, Algorithmic Pricing and Collusion , 2018, American Economic Review.

[6]  Bruno Salcedo.  Pricing Algorithms and Tacit Collusion , 2015 .

[7]  R. Neck,et al.  Conflict and cooperation in a model of stabilization policies : A differential game approach , 1987 .

[8]  H. Lilliefors.  On the Kolmogorov-Smirnov Test for the Exponential Distribution with Mean Unknown , 1969 .

[9]  Anil Aswani,et al.  Statistics with set-valued functions: applications to inverse approximate optimization , 2017, Math. Program..

[10]  S. Hart,et al.  Handbook of Game Theory with Economic Applications , 1992 .

[11]  Vishal Gupta,et al.  Data-driven estimation in equilibrium using inverse optimization , 2013, Mathematical Programming.

[12]  Lixin Ye,et al.  Deciding Between Competition and Collusion , 2003, Review of Economics and Statistics.

[13]  Patrick T. Harker,et al.  Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications , 1990, Math. Program..

[14]  M. Whinston,et al.  Coalition-Proof Nash Equilibria I. Concepts , 1987 .

[15]  Bruce E. Hajek,et al.  VCG-Kelly Mechanisms for Allocation of Divisible Goods: Adapting VCG Mechanisms to One-Dimensional Signals , 2006, 2006 40th Annual Conference on Information Sciences and Systems.

[16]  William Vickrey,et al.  Counterspeculation, Auctions, And Competitive Sealed Tenders , 1961 .

[17]  P. Pardalos,et al.  Equilibrium problems : nonsmooth optimization and variational inequality models , 2004 .

[18]  A. Federgruen,et al.  How Much is a Reduction of Your Customers’ Wait Worth? An Empirical Study of the Fast-Food Drive-Thru Industry Based on Structural Estimation Methods , 2011 .

[19]  Martin Pesendorfer.  A Study of Collusion in First-Price Auctions , 2000 .

[20]  Christo Wilson,et al.  An Empirical Analysis of Algorithmic Pricing on Amazon Marketplace , 2016, WWW.

[21]  Zuo-Jun Max Shen,et al.  Inverse Optimization with Noisy Data , 2015, Oper. Res..

[22]  Zhu Han,et al.  Coalitional game theory for communication networks , 2009, IEEE Signal Processing Magazine.

[23]  Emilio Calvano,et al.  Algorithmic Pricing What Implications for Competition Policy? , 2018, Review of Industrial Organization.

[24]  John M. Staatz,et al.  The cooperative as a coalition: A game-theoretic approach , 1983 .

[25]  Joseph Greenberg,et al.  Chapter 37 Coalition structures , 1994 .

[26]  John N. Tsitsiklis,et al.  Efficiency of Scalar-Parameterized Mechanisms , 2008, Oper. Res..

[27]  Joseph Farrell.  Communication, coordination and Nash equilibrium , 1988 .

[28]  F. Massey.  The Kolmogorov-Smirnov Test for Goodness of Fit , 1951 .

[29]  R. Porter,et al.  Detection of Bid Rigging in Procurement Auctions , 1992, Journal of Political Economy.

[30]  Walid Saad,et al.  Coalitional Game Theory for Cooperative Micro-Grid Distribution Networks , 2011, 2011 IEEE International Conference on Communications Workshops (ICC).

[31]  Jean-Francois Richard,et al.  Bidder Collusion at Forest Service Timber Sales , 1997, Journal of Political Economy.

[32]  Demosthenis Teneketzis,et al.  A Surrogate Optimization-Based Mechanism for Resource Allocation and Routing in Networks With Strategic Agents , 2019, IEEE Transactions on Automatic Control.

[33]  E. H. Clarke.  Multipart pricing of public goods , 1971 .

[34]  Theodore Groves,et al.  Incentives in Teams , 1973 .

[35]  T. Severini.  Likelihood Methods in Statistics , 2001 .

[36]  John Rust,et al.  Structural estimation of markov decision processes , 1986 .

[37]  C. L. Benkard,et al.  Estimating Dynamic Models of Imperfect Competition , 2004 .